“Competitive Targeted Advertising with Price Discrimination” Rosa-Branca Esteves Joana Resende
NIPE WP 08/ 2011
“Competitive Targeted Advertising with Price Discrimination”
Rosa-Branca Esteves Joana Resende
NIPE* WP 08/ 201 1
URL: http://www.eeg.uminho.pt/economia/nipe
*
NIPE – Núcleo de Investigação em Políticas Económicas – is supported by the Portuguese Foundation for Science and Technology through the Programa Operacional Ciência, Teconologia e Inovação (POCI 2010) of the Quadro Comunitário de Apoio III, which is financed by FEDER and Portuguese funds.
Competitive Targeted Advertising with Price Discrimination Rosa-Branca Esteves
Joana Resende
Universidade do Minho (EEG) and NIPE
Faculdade de Economia do Porto
[email protected]
[email protected]
March 2011 (In progress)
Abstract This paper investigates the e¤ects of price discrimination by means of targeted advertising in a duopolistic market where the distribution of consumers’preferences is discrete and where advertising plays two major roles. It is used by …rms as a way to transmit relevant information to otherwise uninformed consumers, and it is used as a price discrimination device. We compare the …rms’optimal marketing mix (advertising and pricing) when they adopt mass advertising/non-discrimination strategies and targeted advertising/price discrimination strategies. If …rms are able to adopt targeted advertising strategies, we …nd that the symmetric price equilibrium is in mixed strategies, while the advertising is chosen deterministically. Our results also unveil that as long as we allow for imperfect substitutability between the goods, …rms do not necessarily target more ads to their own market. In particular, …rms’optimal marketing mix leads to higher advertising reach in the rival’s market than in the …rms’own market, provided that advertising costs are su¢ ciently low in relation to the consumer’s reservation value. The comparison of the optimal marketing-mix under mass advertising strategies and targeted advertising strategies reveals that targeted advertising might constitute a tool to dampen price competition. In particular, if advertising costs are su¢ ciently low in relation to the value of the goods, we obtain that average prices with non-discrimination (mass advertising) are below those with price discrimination and targeted advertising (regardless of the market segment). Accordingly, when (i) goods are imperfect substitutes, (ii) advertising is not too expensive, and (iii) targeted advertising constitutes an e¤ective price discrimination tool, price discrimination through targeted advertising may be detrimental to social welfare since it boosts industry pro…ts at the expense of consumer surplus. We are grateful to Jose Luis Moraga, Emmanuel Petrakis, Simon Anderson and participants of the III Conference on the Economics of Advertising and Marketing (IESE, Barcelona 2010). Financial support from the Portuguese Science Foundation is gratefully acknowledged. Any errors are our own responsability.
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1
Introduction
In many markets …rms need to invest in advertising to inform potential consumers about the existence and price of their new products. The informative view of advertising claims that the primary role of advertising is to transmit information to otherwise uninformed consumers.1 Until very recently, the scope of targeted advertising was relatively limited and …rms tended to privilege an advertising strategy “above the line”, as …rms’ advertising strategies were mostly tailored to mass audiences. However, advertising markets are experiencing a number of deep and fast changes, which are challenging conventional wisdom regarding optimal advertising and pricing strategies. One of the most striking challenges concerns the di¤usion and the widespread use of targeted advertising technologies, which allow …rms to target their messages to particular market segments (see Bagwell, K. (2005)). Targeting advertising strategies are becoming more and more attractive to …rms. One the one hand, the advances in information technologies are enabling …rms to send progressively more accurate advertising messages since such information technologies facilitate the process of gathering, storing and processing consumer-speci…c data. This increases …rms’ability to target di¤erent marketing strategies, e.g. pricing and advertising, to consumers with di¤erent pro…les. On the other hand, the prosperity of electronic markets and the breakthrough developments of new media industries are expected to exponentially enhance the reach of targeted advertising messages. Thus …rms are investing more and more in advertising strategies “below the line” in order to target advertising messages at individuals according to their needs or preferences. For example, expenses below the line advertising media, such as search-related online advertising are growing exponentially.2;3 These expenses are expected to growth substantially in the future following the expansion of electronic markets and the development of new targeted advertising technologies (e.g. the advertising platform iAd developed by Apple).4 From advertisers’perspective, targeted advertising is indeed a very powerful tool. Not only because it can minimize wasted advertising but mainly because target advertising makes the value of advertising more measurable by allowing …rms to adjust their advertising messages to consumers’pro…les. Therefore, apart from its informative role, advertising might be used by …rms as a price 1
In contrast, the persuasive view of advertising holds that the main role of advertising is to increase a consumer’s willingness to pay for the advertised product. In this sense, …rms may use advertising to alter consumers’tastes and to increase brand loyalty. For a review of models in the persuasive view see Bagwell’s (2003) comprehensive survey on the “The Economic Analysis of Advertising.” 2 Examples of search-related online advertising include: Google - AdWords and AdSense; eBay – AdContext; Yahoo!; MSN - adCenter. 3 According to Evans, in 2007, online advertising expenses already represented about 7% of total advertising expenses in the United States (with online advertising expenses amounting to 21 billion of USD). 4 On Apple’s webpage we may read: “iAd is a breakthrough mobile advertising platform from Apple. With it, apps can feature rich media ads that combine the emotion of TV with the interactivity of the web. For developers, it means a new, easy-to-implement source of revenue. For advertisers, it creates a new media outlet that o¤ ers consumers highly targeted information”.
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discrimination device. While economists have long been concerned with understanding the competitive and welfare e¤ects of either price discrimination or informative advertising, little theoretical attention has been dedicated to the interaction between informative targeted advertising and price discrimination. This paper is a step understanding of to the understanding of the competitive and welfare e¤ects of price in an informative advertising model. The main theme of this paper is to investigate the competitive and welfare e¤ects of price discrimination by means of targeted informative advertising. We aim to investigate the social desirability of targeted advertising technologies, investigating how the availability of these technologies may a¤ect …rms’optimal marketing mix (pricing and advertising) and the corresponding level of pro…ts, consumers’surplus and social welfare. To this end, we propose a static game of duopoly competition, in which two …rms, A and B are launching two new di¤erentiated products and need to invest in advertising to generate awareness. Consumers’ heterogeneity is modeled in line with Shilony (1977). Consumers are either loyal (to a speci…c degree, i.e., > 0) to one …rm or the other. Both …rms know that half of consumers have a relative preference for A while the remaining have a relative preference for B. As Raju, et al. (1990), can be used as a measure of the degree of a consumer’s brand loyalty, de…ned as the minimum di¤erence between the prices of the two competing brands necessary to induce consumers to buy the wrong brand.5 This means that full informed consumers will buy from the most preferred …rm as long as its price is not undercut by more than : As in Stahl (1994) a potential consumer cannot be an actual buyer unless …rms invest in advertising. By investing in advertising …rms endogenously segment the market into captive (partially informed) and selective (fully informed) customers. Two advertising strategies are studied in the paper: a mass advertising strategy and a targeted advertising strategy. If …rms use a mass advertising they choose an intensity of advertising to the entire market and send ads with same content (i.e., all ads have the same price) to the entire market. In this case they are forced to follow a uniform pricing policy. In contrast, under targeted advertising …rms choose di¤erent levels of advertising to each market segment and ads tailored to di¤erent segments quote di¤erent prices. When …rms use a mass advertising strategy, and the reservation value is high enough the model yields a symmetric equilibrium in mixed strategies in prices with the advertising component chosen deterministically. In comparison to a full information case (Shilony (1977)) imperfect information boots …rm’s pro…ts and reduces consumer surplus and welfare. When v is high enough we also …nd that pro…ts increase with advertising costs increases. When price discrimination by means of targeted advertising is allowed some new and interesting results arise. The paper shows the price equilibrium is always in mixed strategies and the level of advertising to each segment is chosen deterministically. We show that when the 5
Even though the paper considers that the market is segmented according to brand loyalty, the model also accommodates other interpretations as search costs, transportation costs and switching costs. In the location interpretation, consumers can purchase costlessly from neighbourhood …rms, but incur a transport cost > 0 when buying from more distant …rms.
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advertising costs are high (or v is low) …rms advertise more to its own market. In contrast, we show that when advertising is cheap (and v is high) …rms advertise more to the rival’s market. As in other models with price discrimination based on customer recognition we show that a …rm charges on average lower prices to the rival’s customers than to its own customers (e.g. Thisse and Vives (1988), Fudenberg and Tirole (2000). The stylised model addressed in this paper brings new insights to the literature on price discrimination based on customer recognition. First, we show that average prices with mass advertising (non-discrimination) are below those with targeted advertising. This is an interesting …nding as it challenges the usual …nding that price discrimination may reduce all segment prices. Second, we show that price discrimination by means of targeted informative advertising do not necessarily lead to the classic prisoner dilemma result that arises in models with full informed consumers. In this way we show that at least when v is high and advertising is not expensive each …rm’s pro…t with perfect targeted advertising and price discrimination is above its nondiscrimination counterpart. Finally, another theme of the paper is to investigate the welfare e¤ects of targeted advertising with price discrimination. We show that at least when advertising costs are not too high in comparison to v; price discrimination by means of targeted advertising suggest boost industry pro…t at the expense of consumer surplus and welfare. Thus, the paper highlights the importance of taking into account di¤erent forms of market competition when public policy tries to evaluate the pro…t and welfare e¤ects of price discrimination. Related literature This paper is mainly related to two strands of the literature, namely the literature on competition with informative advertising and the more recent literature on price discrimination based on customer recognition. Following the seminal work of Butters (1977), a vast literature has investigated competition with informative advertising. In a competitive market for a homogeneous product, where advertising is the sole source of information to uninformed customers, Butters shows that the equilibrium is characterized by price dispersion and that the equilibrium level of advertising is socially optimal. The latter puzzling result was con…rmed by Stahl (1994), who extended Butters’ model to oligopolistic markets with more general demand curves and advertising technologies. Variations on Butters’ model, such as the introduction of product di¤erentiation (Grossman and Shapiro (1984)), or heterogeneity among buyers (Stegeman (1991)), were shown to easily o¤set this result. They also helped to establish the idea that increased competition stimulated additional advertising— the business stealing e¤ect— while the incapability of the …rm to appropriate the social surplus it generates acts as a deterrent to advertising — the nonappropriability of social surplus e¤ect (Tirole (1988)). Our paper is more closely related to oligopoly models of advertising with product di¤erentiation, e.g. Grossman and Shapiro (1984); or Stegeman (1991). These papers have shown that equilibrium level of advertising may not be socially e¢ cient in a context of product di¤erentiation or heterogeneity among consumers (in contrast with the results pointed out by Butters (1977) or Stahl (1994) in the context of a competitive market for a homogeneous good). These papers have also put forward the idea of “business stealing 4
e¤ect”6 and “the non-appropriability of social surplus e¤ect” (see also Tirole (1988)).7 The literature on targeted advertising is relatively recent. This literature is evolving along two major lines. The …rst strand of literature corresponds to the literature studying the e¤ects of targeted advertising technologies on prices and competition when …rms can directly target di¤erent consumers.8 The second strand of literature assumes that …rms are not able to directly target their messages to di¤erent groups of consumers, taking into consideration the intermediary role played by media.9 As we assume in this paper that …rms have the ability to directly target their advertising messages to speci…c groups of consumers (which tends to be the case in electronic markets, for example), our paper is more closely related to the …rst strand of literature, speci…cally to Iyer, Soberman and Villas-Boas (2005) and Galeotti and Moraga-González (2008). Iyer et al. (2005) develop a model in which …rms face two types of consumers: captive consumers and shoppers (who are not loyal to any of the …rms, always buying the less expensive good). They show that targeted advertising leads to higher pro…ts regardless of whether …rms have or not the ability to adopt price discrimination strategies. They also conclude that when …rms are endowed with a quadratic targeted advertising technology, they always advertise more in the segment of consumers with a strong preference for its own good. This is in contrast with our …nding that if v is high enough …rms advertise more to the group of consumers with a low preference for its good. As far as concerns the total amount of advertising expenses, this paper concludes that target advertising may either increase or decrease advertising costs when compared with a mass advertising technology.10 Galeotti and Moraga-González (2008) studies …rms’ advertising and pricing strategies in a market with homogeneous good, where market segmentation is based on consumer attributes that are completely unrelated to tastes. The paper compares market outcomes under mass advertising with uniform pricing and targeted advertising with price discrimination. Assuming ex-ante that one market segment is more pro…table then the other the paper shows that the possibility of market segmentation may lead to positive pro…ts within an otherwise Bertrandlike setting. In this paper, an increase on advertising costs increases the pro…tability of market segmentation with …rms having unequal sizes. Regarding pricing strategies, in the case of targeted advertising, the paper shows that the price distribution in the less attractive market dominates (in the sense of …rst order stochastic dominance) the price distribution of the other market. The price distribution under mass advertising is in-between these two distributions 6
The business stealing e¤ect refers to advertising enhancing e¤ect generated by an increase in the degree of competition. 7 This e¤ect refers to the advertising deterrence e¤ect generated by incapability of the …rm to appropriate the social surplus it generates. 8 See for example, Iyer, Soberman and Villas-Boas (2005); Galeotti and Moraga-González (2008); Esteban and Hernández (2007); Esteban, Hernández and Moraga-González (2006); Esteves and Guimarães (2008); Chen and Iyer (2002), Roy (2000). 9 See for example, Chandra (2009); Athey and Gans (2009); Gal-Or and Gal-Or (2005); Gal-Or and Gal-Or (2006); Gal-Or, Gal-Or, May and Spangler (2008). 10 In particular, if advertising unit costs are high (low), advertising costs are higher (lower) when …rms own a targeted than a mass advertising technology.
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(again, in the sense of …rst order stochastic dominance).11;12 Finally, the paper is also related to the literature on competitive price discrimination. It is related to those models where, in the terminology of Corts (1998), the market exhibits bestresponse asymmetry.13 In these models pro…t will typically decrease when price discrimination is practiced. A useful model for understanding the pro…t e¤ects of price discrimination in markets with best-response asymmetry is by Thisse and Vives (1988). There are two …rms located at the extremes of the segment [0; 1] : Consumers are uniformly distributed in the line segment and …rms can observe the location (or brand preference) of each individual consumer and price accordingly. The strong (close) market for one …rm is the weak (distant) market for the other …rm. In this setting they show that price discrimination intensi…es competition, all prices fall as well as pro…ts. The …nding that …rms might be worse o¤ when they engage in price discrimination is one of the key di¤erences between monopoly and competitive price discrimination. If we ignore commitment issues, a monopolist is better o¤ when it uses price discrimination. Although with competition price discrimination is a dominant strategy for each …rm, for given prices o¤ered by its rival, when all …rms follow the same strategy they might …nd themselves in the classic prisoner’s dilemma.14 Price discrimination based on customer recognition has been examined also by Bester and Petrakis (1996), Chen (1997), Fudenberg and Tirole (2000), and Esteves (2010). In all of these approaches consumers are perfectly informed, there is no role for advertising and pro…ts fall with price discrimination. Esteves (2009a) departs from this hypothesis by assuming that without advertising consumers are uninformed and …rms have no demand. However, while in Esteves (2009a) consumers are ex-ante identical regarding their preferences for the …rms, here consumers are ex-ante heterogenous. Esteves (2009a) shows that all …rms might become better o¤, even when only one of them can engage in price discrimination. By proposing a framework in which advertising is the consumers’sole source of information about a …rm/product existence 11
Esteban and Hernandez (2007) study targeted advertising in an oligopolistic market with vertical di¤erentiation. The authors show that the possibility of targeting advertising with price discrimination may lead to permanent segmentation of the market. From a welfare perspective, targeted advertising is shown to have a positive e¤ect on consumers’surplus and social welfare. 12 Other papers studying targeted advertising include Brahim, Lahmandi-Ayed and Laussel (2010), Roy (2000), Gal-Or and Gal-Or (2006); Gal-Or, Gal-Or, May and Spangler (2008). Brahim et al (2010) develop an extended version of Grossman and Shapiro (1984) with targeted advertising, concluding that …rms prefer to target their natural market when advertising costs are low, while they cross-advertise if advertising costs are high. The authors also show that targeted advertising not always has a positive e¤ect on …rms’advertising pro…ts. Roy (2000) studies optimal advertising choices when …rms can target consumers on the basis of their address (i.e. their location on a Hotelling framework). Gal-Or and Gal-Or study the competitive e¤ects of targeted advertising when a single media content distributor delivers advertising messages on the behalf of …rms. Gal-Or, Gal-Or, May and Spangler (2008) deal with the issue of imperfect advertising tailoring, studying to which extent an advertiser should allocate resources to increase the quality of its targeting. 13 The market exhibits best response asymmetry when one …rm’s “strong”market is the other’s “weak”market. In the literature of price discrimination, a market is designated as “strong” if in comparison to uniform pricing a …rm wishes to increase its price there. The market is said to be “weak” if the reverse happens. 14 Esteves (2009b) extends the Thisse and Vives model to a two-dimensional di¤erentiation model and shows that price discrimination might not necessarily lead to the prisoner’s dilemma result. This happens when …rms observe the location of consumers in the less di¤erentiation dimension and price discriminate accordingly while they remain ignorant about their location in the more di¤erentiated dimension.
6
and its price, the paper shows that price discrimination by means of targeted advertising may boost industry pro…t at the expense of consumer surplus and welfare. The rest of this paper is organized as follows. Section 2 describes the main ingredients of the model. Section 3 analyses the benchmark case, in which …rms are endowed with a mass advertising technology that forces …rms to adopt a uniform pricing policy. Section 4 analyses the equilibrium advertising and pricing strategies when …rms are endowed with a targeted advertising technology and price discrimination is permitted. Section 5 stresses the competitive e¤ects of perfect targeted advertising. Section 6 focus on the impact of targeted advertising on social welfare and, …nally, Section 7 sets up the main conclusions.
2
Model Assumptions
Consider a market in which two …rms, A and B, are launching two new products, A and B (respectively). With no loss of generality, we suppose each …rm produces its product at zero marginal cost.15 On the demand side, there is a large number of potential buyers, with mass normalized to one. Each consumer wishes to buy at most a single unit of either good A or B. Goods are di¤erentiated and consumers have heterogeneous preferences in relation to them. In particular, we suppose that the set of potential buyers is composed of two distinct segments of equal mass: market segment a and market segment b: The market segments di¤er one from the other, as a result of consumers’ heterogeneity regarding the relative intrinsic value of good A and good B (within each group, consumers’ preferences are assumed to be homogeneous). In the case of segment a; consumers prefer product A over product B by a degree equal to > 0 : the reservation price of buying good A is equal to v > 0; while the reservation price of buying good B is equal to v > 0: In contrast, consumers belonging to segment b intrinsically prefer product B over product A; whose reservation prices (for consumers in group B) are respectively given by v > 0 and v > 0: The reservation prices (v and v ) are assumed to be su¢ ciently high so that the duopoly equilibrium exhibits competition, i.e. v > pi + ; 8i = A; B: In relation to the parameter ; notice that, as in Shilony (1977), Raju, et al. (1990) and Esteves (2009), can be used as a measure of the degree of a consumer’s preference for the most preferred product. It can also be de…ned as the minimum di¤erence between the prices of the two competing products necessary to induce consumers to buy the least preferred product. This means, for instance, that consumers with a preference for product i will buy product i as long as its price is not undercut by more than by …rm j:16 Consumers are initially uninformed about the existence and the price of the goods. As in Stahl (1994) a potential consumer cannot be an actual buyer unless …rms invest in advertising.17 15
The assumption of zero marginal costs can be relaxed without altering the basic nature of the results derived throughout the model. 16 Raju, et al (1990) present also the case with asymmetric loyalties towards the two …rms. 17 Implicitly we are assuming that for new products search costs are prohibitively high.
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The advertising messages of each …rm contain truthful18 and complete information about the existence of its product and price. After …rms have sent their ads independently (i.e., advertising reach is independent for each …rm), in each segment of the market (a and b); there are, in principle, four di¤erent mutually exclusive and exhaustive categories of consumers. Some consumers are captive to a given …rm (either …rm A or …rm B), because they are are only aware of the existence of one …rm. Other consumers received ads from both …rms and are selective. This latter group of consumers has complete information and will buy from the …rm that o¤ers them the highest surplus. Finally, the remaining consumers are uninformed and excluded from the market as they haven’t received any ad from any of the …rms. The game is static and proceeds as follows. Firms choose advertising intensities and prices simultaneously and non-cooperatively. Under mass advertising …rms choose an intensity of advertising to the entire market and all ads announce the same price. With targeted advertising …rms choose di¤erent levels of advertising to each market segment and ads tailored to di¤erent segments quote di¤erent prices. Advertising technology: Advertising is a costly activity for …rms. The advertising technology is exogenously given and it is the same for both …rms. Two advertising technologies will be used throughout this paper, a mass advertising technology and a targeted advertising technology. When …rms use a mass advertising technology they are also forced to follow a uniform pricing policy which means that all the ads quote the same price. In this case, the problem of …rm i consists in choosing an optimal advertising reach, i ; and the corresponding uniform pricing strategy pi ; i = A; B: The cost of reaching a fraction of consumers is given by the function A( ) = ( ) : Following the literature on informative advertising (e.g. Butters (1977) and Tirole (1988)), it is assumed that the cost of reaching consumers increases at an increasing rate, which formally can be written as A > 0 and A 0.19 The latter condition means that it is increasingly more expensive to inform an additional customer or likewise to reach a higher proportion of customers.20 It is also assumed that there are no …xed costs in advertising, i.e. A(0) = 0: Finally, in order to make advertising viable, it is assumed that A (0) < v: The quadratic technology proposed in Tirole (1988) is not based upon an underlying technology of message production. However, it has the advantage of being extremely simple to manipulate algebraically. It is given by A( ) = ( ) ; where ( ) = 2 : As in the present model there is a large number of buyers, normalized to one, can be identi…ed with the cost per ad. In what 18
This is guaranteed by the FTC regulation that prohibits advertisers from making false and deceptive statements about their products (see www.ftc.gov/bcp/conline/pubs/buspubs/ad-faqs.htm). 19 Subscripts denote partial derivatives. 20 Several justi…cations support this assumption. One justi…cation has to do with the advertising technology itself. In other words, if ads are sent randomly at a …xed cost per ad, then the probability of reaching a consumer not yet informed decreases with the amount already advertised (e.g. the Butters’urn technology and the Constant Reach Independent Readership (CRIR) technology proposed by Grossman and Shapiro (1984)). Thus, as the number of ads sent increases it becomes increasingly costly to inform a consumer who has not yet received an ad from the …rm. Other justi…cations are the existence of di¤erent predispositions to view ads on the part of the target population and the possibility of media saturation.
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follows, whenever a functional form is needed, we will use the quadratic technology. When …rms are able to use targeted advertising, …rms can target ads to speci…c segments of the market. In the context of our model, this amounts to say that each …rm may send two types of ads: ads targeted to the group of consumers who intrinsically prefer its own product and ads targeted to the group of consumers who intrinsically prefer the rival’s product. Within each segment messages are randomly distributed among consumers. On other words, within each group some consumers may receive one ad, more than one or none. In addition, targeted advertising can also be used as a tool for price discrimination since ads targeted to di¤erent segments of the market may quote di¤erent prices. In this case, the problem of …rm i becomes more complex as it must choose an optimal advertising reach and an optimal price strategy to each segment of the market. With respect to advertising, the problem of …rm i consists in an advertising intensity for each segment of the market, oi targeted to its own market and ri targeted to the rival’s market. Ads targeted to each segment will have di¤erent prices, respectively poi and pri ; i = A; B. The parameter oi 2 [0; 1] can be interpreted as the share of consumers in segment i that have received …rm i0 s ads targeted to its own customers. Similarly, ri 2 [0; 1] can be interpreted as the share of consumers who received ads from …rm i; despite preferring the product o¤ered by the rival’s …rm. The cost of reaching a fraction ki of consumers, k = fo; rg, is given by the strictly convex k function A( ki ) = i : It is also assumed that A(0) = 0 and A ki (0) < v: In what follows, whenever a functional form is needed, we will use the advertising technology proposed in Tirole (1988).
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Mass advertising
This section investigates optimal pricing and advertising strategies when …rms are endowed with a mass advertising technology. In this case, …rms follow a uniform pricing policy as they are unable to target ads to speci…c segments of the market. Accordingly, there are two components to a …rm’s strategy: Firm i must choose its advertising level (denoted by i ), as well as its price (denoted by pi ). We start the analysis by investigating consumers’decisions. In each segment of the market (segment a and segment b); it is possible to …nd four mutually exclusive and exhaustive categories of consumers: (i) …rm A0 s captive consumers; (ii) …rm B 0 s captive consumers; (iii) selective consumers; and (iv) uninformed consumers. The latter are uninformed about the existence of both products and therefore they simply do not buy any of the available goods. In contrast, selective consumers are fully informed and they shop for the better bargain. For example, selective consumers in segment a compare the net utility of purchasing good A at price pA ; v pA ; with the net utility of purchasing good B at price pB ; v pB : Such selective consumers buy good A if and only if pA < pB + : Analogously, selective consumers in segment b compare goods’relative utility and they buy good A if and only if pA < pB : Reversing the previous inequalities one gets the conditions under which di¤erent types of selective consumers buy good B. Additionally, each …rm has a group of 9
captive consumers who buy its product as long as pi < v if the consumer is of type i or pi + < v if the consumer is not of type i: The relative size of each group of consumers (captive, selective or uninformed consumers) depends on …rms’decisions with respect to advertising. After …rms have sent their ads independently, a proportion i and j of customers is reached by …rm i and j advertising, respectively. Hence, the potential demand of …rm i is made of a group of captive (locked-in) customers, namely i 1 j ; and a group of selective customers, namely i j , i = A; B; j = A; B: In the light of this, when pi < v ; 8i = A; B; the demand for good i when …rms are endowed with a mass advertising technology, Di ; is equal to: 2 3 1 4 1 Pr (pi Di = i 1 < pj ) + Pr (pi + < pj )5 (1) j + i j 2 2 captive selective type i
selective type j
Firm i0 s expected pro…t is equal to
E
i
= pi Di
A ( i)
(2)
Given the rival’s strategies, j and pj ; the problem of …rm i consists in choosing the advertising intensity, i , and the pricing policy, pi that maximize its pro…t, pi Di A ( i ) :
3.1
Equilibrium Analysis
In this section, we study equilibrium price and advertising strategies, concentrating the analysis on the symmetric Nash equilibrium. Proposition 1 points out the conditions under which a symmetric price equilibrium in pure strategies exists.
Proposition 1 (i) When v < 2 then a pure strategy equilibrium exists with pi = pj = v: (ii) When 2 < v < 3 ; there is a symmetric price equilibrium in pure strategies with p i = pj = v ; as long as j < 1 v : (iii) When v > 3 then there is no pure strategy equilibrium in prices. There is however a mixed strategy Nash equilibrium in prices. Proof.
See the Appendix.
In what follows we characterize the symmetric Nash equilibrium in prices. Firs we study cases (i) and (ii), in which …rms do not compete for selective consumers (monopoly cases). Then, we address case (iii), in which …rms compete for selective consumers (duopolistic competition).
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3.1.1
Monopoly cases
In this section there are two relevant symmetric cases where …rms act as local monopolists. The …rst case corresponds to situation (i) in Proposition 1 in which …rms charge a price equal to v; as they exclusively serve the segment of the market with a strong preference for its good. In this case, …rms charge a price equal to v in order to extract all the surplus from its customers and, as a result, some consumers stay out of the market after being exposed to advertising. The second case corresponds to situation (ii) in Proposition 1. In this case …rms charge a price equal to v ; and we observe that both …rms serve all captive consumers, sharing evenly selective consumers. Accordingly, in this case, all informed consumers can enter the market. Firms have the monopoly provision of the good to its captive consumers and they choose not to compete for the selective consumers. Case 1: (pi = v; pj = v) Consider …rst the case where v < 2 : In line with Shilony (1977) if v 2 ; we obtain that, in equilibrium, both sellers charge a price v and so each …rms acts as a monopolist in its strong market segment (corresponding to the segment of consumers whose reservation price for the good o¤ered by the …rm is equal to v). It is therefore straightforward to obtain that …rm i’s equilibrium pro…t is i
1 = v 2
i (1
j)
+
1 A ( i) = v 2
i j
The equilibrium level of advertising is obtained maximizing we obtain 1 v = A ( i) 2 and A (0) > 12 v: Equilibrium pro…ts are in this case equal to i
=
A (
)
A(
i
A ( i)
i
in order to
i:
From the F OC
):
For the quadratic technology for instance we would obtain =
v with v < 4 4
and thus
v 2 : 4 Given the …rms’price and advertising choices, when v < 2 ; total welfare is equal to: i
W
= v = v
h
=
(1 2A (
)+( )
)2
i
Since industry pro…t is equal to ind
=v
2A ( 11
);
2A (
)
it follows that expected consumer surplus is equal to zero. As a matter of fact, in this case, the price quoted by …rms corresponds to the reservation price of consumers with a strong preference for their good (v) and …rms extract all the surplus from their customers (in addition, there are some consumers who stay out of the market after being exposed to advertising). For the quadratic technology W =
ind
=v
v 4
2
v 4
2
=
1 v2 8
and CS = W
2 = 0:
Case 2: (pi = v ; pj = v ) In this case, …rms charge a price corresponding to the reservation price of consumers with a weakest prference for their good (equal to v ). In the light of this pricing strategy, …rms sell all their captive consumers and they share the selective consumers. Here …rm i’s equilibrium pro…t is i
= (v
)
i (1
j)
+
1 2
A ( i) =
i j
(v
) i
2
2
A ( i)
j
The equilibrium level of advertising is obtained maximizing i in order to i ; from which we obtain (v ) 2 j = A ( i) 2 Given the symmetry of the problem it must be the case that i = j = : Thus, the equilibrium level of advertising is given by (v
) (2 2
)
=A (
)
as long as , it is always true that obtains:
)
> 0: We only need to impose that
< 1 from which one
v 3 …rms compete to attract selective consumers. From lemma 1 we can establish the next lemma.
13
Lemma 2. In order to be able to serve all captive consumers, for each …rm i;we must observe pi;max v . From Proposition 1 we already know that when v > 3 an equilibrium in pure strategies fails to exist. The intuition for the inexistence of a pure strategy price equilibrium is when v is high enough or is low enough, the existence of a positive fraction of selective consumers with a preference for the rival …rm creates a tension between the …rm’s incentives to price low in order to attract this latter set of customers and …rm’s incentives to price high as a way to extract rents from the group of its captive and selective loyal customers. Therefore, each …rm follows a mixed pricing strategy as an attempt to prevent the rival from systematically predicting its price, which in turn makes undercutting less likely. In this section, we investigate the mixed strategy Nash equilibrium in prices when …rms compete for selective consumers, with pmax < v : Proposition 2 bellow characterizes this equilibrium, pointing out the conditions under which such equilibrium exits. In the Appendix we prove by construction that there is a symmetric mixed strategy equilibrium in prices in which …rms compete for selective consumers, with pmax < v . Suppose that …rm i selects a price randomly from the cdf Fi (p): In a symmetric mixed strategy equilibrium, both …rms follow the same pricing strategy, thus, for the sake of simplicity write Fi (p) = Fj (p) = F (p). Suppose further that the support of the equilibrium prices is [pmin ; pmax ] with pmax < v : When …rm i charges price p; there are three relevant outcomes. Firstly, p can be low enough to make all selective consumers interested in buying good i. This event occurs with probability 1 F (p + ) : Secondly, p can be such that each …rm sells to the group of selective consumers with a preference for its product. This event occurs with probability [F (p + ) F (p )] : Finally, p can be so high that …rm i is unable to attract any selective consumers, only serving the group of captive consumers. Hence, for a given i and j ; when …rm i charges price p < v ; …rm i’s expected pro…t, denoted E i ; is E
i
=p
1
i
j
+p
1
i j
In the mixed strategy nash equilibrium, for a given satis…es: E
i
=p
i
1
j
+p
1
j
i j
1
+p
i j
1 Fj (p 2
1 Fj (p + ) 2
1 Fj (p + ) 2
i
1 Fj (p 2
and
)
)
j;
A( i ):
each …rm expected pro…t
A( i ) = k
or equivalently: p
i
1
1 Fj (p + ) 2
14
1 Fj (p 2
) = k:
A( i ):
Proposition 2. In the benchmark case, with a mass advertising technology and no price discrimination, as long as pmax < v (i) each …rm’s price is randomly chosen from the cdf given by 8 > > > > > < 1
m
F (p) =
0 2
> 2 > > > > :
with
(
m 2
(
m 2
)
2 )
if
km p+ km p
m
(1
m
)
if
pmin 5 p 5 pmax
m
(1
m
)
if
pmax
1
pmin = pmax
p < pmin
5 p < pmax > > > > > ; p=p
if 2k m m (2
2 and pmax =
9 > > > > > =
max
m
)
+
From k m =
m
2
0
m
2
@1 +
m
(pmax
m
) (2 km =
2
(2
s
1+
)
1+
1+
m
(ii) Each …rm chooses an advertising reach
m
m
=
A (
m
2
m m
2
1
A:
2 [0; 1]; implicitly given by:
1 m (pmax ) (2 )=A ( 2 (iii) Each …rm earns an overall expected pro…t equal to E
1
A+2
m
2
) we obtain that: 0 s m 2@
2
m
)
m
A(
m
)
(4)
)
(5)
or, equivalently, E
Proof.
qm
m
=
2
(2
0
m 2@
)
1+
s
2
m
1+
2
m
1 A
A(
m
):
See the Appendix.
Proposition 3. 2 [0; 1]: q
m
Each …rm serves its group of selective customers with probability given by
=1
" 8 (k m )2 ln ( m )4
(pmax )2 pmax (pmax 2 )
15
!
1 (pmax
)2
#
:
Proof.
See the Appendix.
Quadratic Technology: Next we study the …rms’advertising and pricing strategies when the advertising technology is the quadratic one. This technology has been also used in other papers studying targeted advertising, e.g. Iyer and Villas-Boas (2005) and Galeotti et al (2008). Although this technology is not based upon an underlying technology of message production, it has the advantage of being extremely simple to manipulate algebraically. It is given by A( ) = ( ) ; where ( ) = 2 : As in the present model there is a large number of buyers, normalized to one, can be identi…ed with the cost per ad. Under these assumptions, we now investigate the …rms’advertising and pricing strategies. 2 For the quadratic technology A ( ) = 2 = and A ( ) = 2 : From (4) it follows that if pmax < v the equilibrium level of advertising is implicitly given by:
2
0
0
@(2
)2 @1 +
s
2
1+
11
AA = 2
2
When v is su¢ ciently high such that pmax < v and the advertising technology is the quadratic one the equilibrium level of advertising is given by p 8 + 2 2 2 + 16 8 m : (6) = 2+8 16 2 In the context of the advertising technology A ( ) = 2A ( ) : Thus E
m
=
1 2
m
A (
m
)=
(
m 2
) > 0:
When v is high enough thatpis pmax < v and the advertising technology ( 2+1) 2 m is the quadratic one, i.e. A ( ) = ; if > then 2 (0; 1) : 4 Proposition 4.
Proof.
See the Appendix.
In the following …gure, we illustrate …rms’optimal advertising reach when …rms are endowed with a quadratic mass advertising technology.
16
MRA, MCA
10
MRA
MAC'
5
MAC
0 0.2
0.4
0.6
Mass advertising technology:
0.8
1.0
Advertising m
:
The downward sloping curve MRA is the marginal revenue of advertising with mass advertising i.e., the left hand-hand side of equation (4). The MRA is plotted for the case where = 1 and for v high enough i.e., for v > pmax + : The upward sloping curves are the marginal cost of advertising for the quadratic technology for the special case where = 2 (MCA) and = 3 (MCA’). Shifts in the latter curve are only due to changes in : We can see that an increase (decrease) in marginal advertising costs makes the curve move upwards (downwards) and gives rise to less (more) advertising in equilibrium.21 The intersection between the MRA and a MCA curve provides the equilibrium level of advertising with mass advertising. When = 2; the p m 16 17 34 which is approximately equal to equilibrium level of advertising for each …rm is = 47 p 22032 4352 17 m which is approximately equal to 1:85: 0:68: In this case k = 2209 pmax = which implies that v >
p
2k m m (2
m
)
+1=
p
17 + 1 < v
1
17 + 2: Equilibrium pro…t is in this case equal to !2 p 16 17 34 E m=2 = 0:925 36: 47
In this case qm = 0:7694: When = 3 and = 1 the equilibrium level of advertising for each …rm is m = 10 17 which is 10 2 m approximately equal to 0:588: In this case E = 3 17 = 1:038 1 and pmax ' 6; thus v > 7: Firms share the selective group of consumers with probability equal to q m = 0:763:
3.2
Welfare Analysis
Next we compute total welfare with mass advertising. Recall that customers’ gross bene…t of buying a certain good can be given by v “expected disutility cost”, where the latter is equal 21
To be precise, because A
> 0 and A
0; static comparative analysis shows that
17
@ m @
< 0.
to ; when the consumer buys the least preferred good; and zero, when the consumer buys the most preferred good. In the social optimal solution, consumers would buy from the most preferred …rm, in order to obtain a gross bene…t of v (and minimize the expected disutility cost). However, in a symmetric equilibrium such outcome can only be reproduced if …rms (i) share equally the group of selective consumers; and (ii) …rms’ captive consumers are those with a stronger preference for its own good . Otherwise, there is always a group of consumers who buy their least preferred good, thereby supporting a kind of disutility cost, i.e. : Accordingly, total welfare can be represented as: h i m 2 W m = v 1 (1 ) EDC m 2A( ); (7) where EDC m stands for the expected disutility costs in the mass advertising/no discrimination case with pmax < v ; 3 2 6 4
EDC m =
m
m
(1
)+
captive
1 (1 2
7 q m )5
(8)
selective
The function EDC m re‡ects the fact that market outcomes in the context of mass advertising/ no discrimination may not be fully e¢ cient as some consumers may buy from the least preferred …rm. The function EDC m has two components. The …rst component refers to the disutility supported by captive consumers who are only aware of the least preferred product, i.e. m m (1 ) : The second component refers to the disutility supported by selective consumers who bought the least preferred version of the good as a result of …rms’ pricing decisions. Recalling that q m represents the probability of demand sharing with mass advertising, we may say that, under non discrimination, all selective consumers buy e¢ ciently with probability equal to q m : With probability 1 q m , half of selective consumers buy ine¢ ciently and the remaining buy e¢ ciently. Accordingly, the expected disutility cost supported by selective consumers is simply: 1 qm) : 2 (1 Plugging (8) in (7), total welfare can be re-written as: W
m
h
=v 1
(1
m 2
)
i
For the numerical example where
m
= 1;
m
(1
)+
1 (1 2
= 2; q m = 0:7694;
W m = 0:89773v
2:1835:
As for this numerical example we should observe that v > Industry pro…ts are in this case equal to: m ind
=4
p 16 17 47
18
34
!2
p
qm) m
=
2A(
m
p 16 17 34 47
):
(9)
we that: (10)
17+2 it follows that W m & 3:313.
' 1:8507:
Thus, expected consumer surplus is equal to: ECS m = W m
m ind
(11)
Thus, ECS m & 1:462: 2 10 For the case where = 3, = 1 we have m = 17 , E m = 3 10 = 1:038 1 and pmax = 6; 17 thus v > 7: Firms share the selective group of consumers with probability equal to q m = 0:763: Total welfare equals: W m = 0:83045v 2: 436 8: (12) As v > 7 then W m & 3:376 4: Industry pro…ts are m ind
= 2:076
ECS m = W m
m ind
& 1:3004:
Comparing equations (10) and (12), we conclude that, as expected, for a given reservation price v; social welfare is larger when = 2 than when = 3: The same is true for consumers’ surplus. For example, if for comparison purposes, we take v = 7; we observe that W m=2 = m = 2: 249 9; with ECS m m 4: 100 6; and ECS m=2 = W m ind =2 > ECS =3 : However, …rms do not necessarily bene…t from having a more e¢ cient advertising technology. In fact, for the values of the parameters considered in the example above, we observe that: m=2 < m=3 : The rationale for this result lies on the competition-dampening e¤ects associated with a less e¢ cient advertising technology. By making advertising more expansive, a increase in , reduces …rms’ advertising intensity (e.g. in the context of our examples m=2 > m=3 ), with a direct negative e¤ect on pro…ts. However, the decline in …rms’ advertising intensities diminishes consumers’ awareness of the product, shrinking the group of selective consumers. As a result, …rms prefer to focus on the group of captive consumers, relaxing price competition (with a positive e¤ect on pro…ts). For the values of the parameters we considered in this example, we observe that the anti-competitive e¤ect following an increase of more than compensates the direct negative e¤ects stemming from an increase in advertising marginal costs.
4
Targeted advertising and price discrimination
This section investigates …rms’advertising and pricing decisions when …rms have the possibility to target ads to speci…c segments of the market and therefore …rms may use advertising strategies as a tool for price discrimination. Now …rm i0 s strategy is to choose the levels of advertising to be targeted to its own and to the rival’s market ( oi and ri ; respectively) and the prices to be quoted to each group of consumers (poi and pri ; respectively). In this paper, we assume that …rms’targeting ability is perfect, i.e.: Pr(fall in i j targeted to i) = 1 Pr(fall in i j targeted to j) = 0; 19
which means that all messages targeted to group i; j = A; B fall in the targeted segment and therefore there is no leakage of ads between groups. The following table clari…es consumers’ information regarding prices contingent on …rms’ advertising strategies. pki
% Type a consumers who know pki
% Type b consumers who know pki
o A
poA prA poB prB
0
0
r A o B
r B
0
0
Since there is no leakage of ads between di¤erent market segments, type a consumers are only aware of poA and prB ; since the remaining pricing strategies, prA and poB are quoted in the ads that are targeted to type b consumers. Again, in each segment of the market potential consumers can be divided into captive, selective and uninformed consumers. In market segment i; after …rms have sent their ads independently, a proportion oi and rj of customers is reached, respectively, by …rm i and j advertising. Thus, the …rm i0 s demand in this segment of the market is made of a group of captive (lockedr o r in) customers, namely oi 1 j ; and a group of selective customers, namely i j , i = A; B; j = B; A: In the light of this, …rm A0 s sales in segment a (at price poA ) are equal to: 3 2 1 1 r o r o Pr(poA < prB + )5 DA = 4 oA (1 B) + 2 2 A B captive
type a selective
and …rm A0 s sales in segment b (at price prA ) are equal to: 2 1 1 r o r o Pr(prA + DA = 4 rA (1 B) + 2 2 A B captive
3
< poB )5
type b selective
Similarly, …rm B 0 s sales in segment a (at price prB ) are given by 2 3 1 1 r o r o DB = 4 rB (1 Pr(poA > prB + )5 A) + 2 2 B A captive
type a selective
and …rm B 0 s sales in segment b (at price poB ) are equal to: 2
o DB =4
1 2
o B
(1
captive
r A)
+
1 2
o r r B A Pr(pA
+
3
> poB )5
type b selective
As there is no leakage, segments are totally independent. For a given strategy of the rival …rm, …rm i0 s expected pro…t conditional on ads and prices targeted to segment k = o; r; is equal to E ki = pki Dik A ki ; i = A; B; and k = o; r: 20
Recall that, even when targeting is perfect, there always exist captive and selective consumers in each segment of the market. Look …rst at segment a. Within this segment, captive consumers to …rm A are only aware of poA ; while the captive consumers to …rm B are only aware of prB : The selective consumers in segment a are aware of poA as well as prB : The same applies mutatis mutandis to segment i. Therefore, …rm i’s expected pro…t in its own segment, denoted E oi ; is given by: E
o i
= poi
o i
r j
1
2
r j
+
Pr(poi < prj + )
A(
with i = A; B; and j = B; A: Similarly, …rm i0 s expected pro…t in the rival’s market, denoted E E
r i
= pri
r i
o j)
(1
2
o j Pr
+
pri +
< poj
A(
o i);
r; i
(13)
is given by:
r i):
(14)
In each segment k; given …rm j 0 s advertising and pricing strategy, …rm i chooses the advertising level ( ki ) and the targeted price (pki ) in order to maximize its expected pro…t de…ned by (13), in the case of its own market segment, and (14), in the case of the rival’s market segment. Proposition 5. Proof.
There is no price equilibrium in pure strategies.
See the Appendix.
Proposition 6. When target is perfect there is a symmetric Nash equilibrium in which: (i) In its own market segment each …rm i; i = A; B chooses a price randomly from the distribution Fio (p) given by 9 8 r > > 0 if p p + > > j min = < h i o (v )(1 ) o 1 r i 1 if pj min + p v Fi (p) = o p i > > > > ; : 1 if p v where prj min = (v
o i ):
) (1
o i
The advertising level 1 v 2
o i
(v
)=A
is implicitly given by o i
(
o i
)
(15)
or equivalently, 1 v=A 2
poimin with A
o i
o i
(
o i
)
(0) < 12 v: Equilibrium pro…t in its own market is: E
i
o
=
i
o
A
i
o
(
i
o
)+
1 ( 2
21
i
o 2
) (v
)
A(
o A ):
(16)
(ii) In the rival’s market segment each …rm chooses a price randomly from the distribution Fir (p) given by 8 9 r > > 0 if p p > > j min > > < = o o v 1 + ( ) j j r 1 r 1 Fi (p) = if pj min p v r p+ i > > > > > > : ; 1 if p v The advertising level
r i
is implicitly given by 1 (v 2
)
1 2
o j
(v
)=A
r i
r i
;
(17)
or, equivalently, 1 r p =A 2 j min where oj solves condition (15) and A rival’s market is: E Proof.
i
r
=
r i
i
(0)
v 2 , otherwise the reverse happens. They choose the same intensity of advertising to both markets when prj min = v 2 : Proposition 7. Regardless the advertising technology considered, when price discrimination is permitted and target advertising is perfect: (i) When advertising is costless, …rms do not select full market coverage in its own market. (ii) When the advertising costs are high, i.e., if is such that oi < v ; …rms advertise more to its own market; when advertising is cheap, i.e., if is such that oi > v ; they advertise more to the rival’s market; …rms choose the same level of advertising to both market segments when is such that oi = v :
22
See the Appendix.
Proof.
o i r i
When
Corollary 1. 1 v < 1:
o i
2 : (i) it is always true thatp oi 2 (0; 1) : (5v 9 )(v ) (v ) (ii) ri 2 (0; 1) i¤ > 8 23
)
(20)
See the Appendix.
Proof.
Proposition 9. With the quadratic technology …rms advertise more to their rival’s market p o 2 + 16 than to their own market, i.e., r when v 21 3 + : The reverse happens p 2 + 16 : when 2 < v < 21 3 + See the Appendix.
Proof.
Adv_Own 0.3 0.2 3.0 2.8 2.6 2.4
12 10
0.1 2.2
2.0
1.8
1.6
Adv. Costs
1.4
8 6
0.0
v
Advertising Intensities in each segment
r
5
Figure 2 shows that when = o : When v is high and
= 1; v = 5 and is low r > o :
= 3 v =
1 2
3 +
p
2
+ 16
and thus
Competitive e¤ects of perfect targeted advertising
This section investigates how targeted advertising and price discrimination a¤ects the equilibrium outcomes— i.e., advertising intensities, prices and pro…ts. Proposition 10 With perfect targeting each wins the group of selective customers in its own market with probability equal to 2 [0; 1] where =
v
Proof:
r
v
1
1
o
(v
o
)
2 pr min
v
(v
See the Appendix.
24
pomin ) + v (
pomin ) ln
pomin v prmin v
:
E¤ects on Prices Figure 3 plots Fim (p) (bold), Fir (p) (dash) and Fio (p) (solid) for the case where = 1; = 2 and v = 7. For this numerical example we observe that F m > F k ; k = o; r; thus F k is stochastically larger than F m implying that in this case average prices with perfect targeting and price discrimination are above average prices with mass advertising and non-discrimination. This is an interesting …nding because a common …nding in the literature on competitive price discrimination is that uniform prices are above the discriminatory ones (e.g. Thisse and Vives (1988), Fudenberg and Tirole (2000). The intuition is that targeted advertising may act to soften price competition. Corollary 3. Regardless the advertising technology considered, as advertising becomes cheaper, the minimum price in the equilibrium support of both cdf Fir (p) and Fio (p) decreases. When advertising becomes costless pomin > : Note that when
o
! 0;
=
v 2(v
and poimin = 21 v >
)
which is true as v > 2 .
E¤ects on pro…ts Firm i’s pro…t with perfect targeted advertising is E For the quadratic technology we have E
i
o
1 ( 2
o
)+
r
= A(
= A(
i
E
i
o 2 A ) (v
t
=E
i
r +E
);
i
o:
(21)
and i
r
):
(22)
Each …rm pro…t with targeted advertising is t
E
= A(
i
o
)+
1 ( 2
o 2 A ) (v
Using the fact that with the quadratic technology we have that: E
t
=
+
v
|
2 (v {z
E
i
o
2
v 2
) + A(
)+4
o
(
2+1) ; 4
)
|
r
and
)+4
) (v + 4 8 (v + 2 {z E
With mass advertising and with the quadratic technology where p
r
v 2(v
(v
+ }
=
i
i
m
=
2 ) )
r
=
2 4
p p8 1
1+ 4
(v
if we take into account that v is high enough to guarantee that pmax < v
2 ) )
2
: }
+ 8
)(v+4 8 (v+2
2
+
2
; and
>
; equilibrium
pro…t is:
E
m
1 = 2
m
A (
m
) = A(
m
)=
2 4
1+
p
1 4
8 p
+ 8
2
+
2
!2
:
(23)
Figure 4 plots equilibrium pro…t with mass (green) and targeted advertising (blue) when = 1 and assuming that v and are such that all the conditions for the equilibrium proposed in proposition 2 (pmax < v ) are met.
25
We can see that when v is large enough in comparison to equilibrium pro…t with perfect targeted advertising is above equilibrium pro…t with mass advertising. 7 For the numerical example where = 1; = 2 and v = 7 it follows that o = 20 and r 39 o r t = 80 . In this case we obtain E i = 0:612 and E i = 0:475. Thus, E = 1:087: In this case, E m = 0:92536: For the numerical example where = 1; = 3 and v = 8 it follows that o 4 63 o 76 r o r = 13 ; r = 21 52 ; pB min = 13 ; pmin = 13 : Thus, E i = 0:615 and E i = 0:489: Thus, E t = 1:104; while in this case E m = 1:0381: These numerical examples show that if we take into account that with mass advertising v > 3 and v is high enough such that pmax < v then if advertising costs are not too high targeted advertising and price discrimination can boost …rms’ pro…ts in relation to the mass advertising/no discrimination case. This is an interesting …nding because it shows that discrimination by means of targeted informative advertising do not necessarily lead to the classic prisoner dilemma result that arises in models with full informed consumers (Thisse and Vives (1988), Fudenberg and Tirole (2000)). In this way we show that at least when v is high and advertising is not too expensive each …rm’s pro…t with perfect targeted advertising and price discrimination is above its non-discrimination counterpart. It is also interesting to note that while with mass advertising while with mass advertising the …rm’s pro…t increases with increases in the advertising costs the reverse happens with targeted advertising. E¤ects on market segmentation o
r
(1 o
r
(1
r
o
v
) =
2 (v v
=
2 (v (v
) =
Non-informed consumers out of the market is given by
(v
1
)+4
(v
) (v + 4 8 (v + 2
)+4
) (v + 4 8 (v + 2
) (v + 4 8 (v + 2
2 ) )
2 ) )
2 ) ) v
1
2 (v
)+4
o
r
) (1
)
while with mass advertising this number of consumers m 2
N I m = (1
) :
With the quadratic technology we have 1
v 2 (v NI
=1
=1
With targeted advertising the number of consumer who stay
N I t = (1
N It =
=1
m
)+4 =
1
(v
1 2 4
1+
p
1 4
26
8 p
8
) (v + 4 8 (v + 2 !2 + 2 +
2
2 ) )
6
Welfare Issues
This section compares aggregate welfare with mass and targeted advertising. As before total welfare can be written as v “expected disutility cost” advertising costs. In the social optimal solution selective consumers should buy from the preferred …rm. With targeted advertising this only happens when a …rm wins the group of selective consumers in its own market, which happens with probability . Similarly, in what concerns captive consumers, we observe that in the social optimal solution, captive consumers would buy from its most preferred …rm. However, at equilibrium, this is nor necessarily the case as some consumers might be captive to their least preferred brand, which introduces an additional source of ine¢ ciency as these consumers buy ine¢ ciently. Accordingly, with perfect targeted advertising overall welfare is given by:
W t = v [1
o
(1
) (1
r
)]
[
r
o
(1
)+
o r
(1
)]
2A (
) (1
qm)
o
)
2A (
r
):
(24)
We have seen that with mass advertising aggregate welfare: h Wm = v 1
(1
m 2
)
i
m
m
(1
)+
1 ( 2
m 2
2A(
m
):
(25)
Expected consumer surplus which is equal to ECS = W
ind :
Table plots industry pro…t, consumer surplus and welfare for thepcase where = 1. When 17 34 = 2 and v = 7 with mass advertising q m = 0:7694 and m = 16 47 : In this case, with r o 39 7 = 80 and = 0:31529: When where = 1; = 2; v = 8, targeted padvertising, = 20 ; m 16 17 34 m = and q = 0:7694 with mass advertising, while with targeted advertising o = 47 r 4 10 = 49 = 0:29228: Finally, when where = 1; = 3; v = 8, m = 17 and q m = 0:786 11 ; 88 ; 4 ; r = 21 = 0:33934: with mass advertising, while with targeted advertising o = 13 52 ; Table 1. Pro…ts, Consumer Surplus and Welfare = 2; v = 7 = 2; v = 8 = 3; v = 8 t ind E m ind Wt
E
2:174
2:694
2:208
1:851
1:851
2:076
3:514
4:361
3:821
Wm
4:162
5:06
4:289
ECS t
1:34
1:667
1:613
ECS m
2:311
3:209
2:212
The numerical examples show that targeted advertising and price discrimination can boost industry pro…t at the expense of social welfare and consumer welfare. This result is therefore in stark contrast with the general presumption of Chen (2005), according to whom “price discrimination under customer recognition ... is by and large unlikely to raise signi…cant antitrust 27
concerns. In fact, as the economics literature suggests, such pricing practices in oligopoly markets often intensify competition and potentially bene…t consumers.” (p. 123). Thus the paper highlights the importance of taking into account di¤erent forms of market competition when try to evaluate the welfare e¤ects of price discrimination based on customer recognition.
7
Conclusions
This paper has investigated the e¤ects of price discrimination by means of targeted advertising in a duopolistic market where advertising plays two major roles: it is used by …rms as a way to transmit relevant information to otherwise uninformed consumers, and it is used as a price discrimination device. Two advertising and pricing strategies were studied in the paper: (i) a mass advertising/nondiscrimination strategy and a targeted advertising/price discrimination strategy. Under mass advertising …rms choose an intensity of advertising to the entire market and all ads announce the same price. With a mass advertising strategy, if the reservation value is high enough the model yields a symmetric equilibrium in mixed strategies in prices with the advertising component chosen deterministically. When price discrimination by means of targeted advertising is used …rms choose di¤erent levels of advertising to each market segment and ads tailored to di¤erent segments quote di¤erent prices. The paper has shown that the price equilibrium is always in mixed strategies and the level of advertising to each segment is chosen deterministically. We have also shown that when the advertising costs are high (or v is low) …rms advertise more to its own market. In contrast, when advertising is cheap (and v is high) …rms advertise more to the rival’s market. As in other models with price discrimination based on customer recognition we showed that a …rm charges on average lower prices to the rival’s customers than to its own customers (e.g. Thisse and Vives (1988), Fudenberg and Tirole (2000). The stylised model addressed in this paper has shown that new insights may arise in the literature on price discrimination based on customer recognition if …rms need to invest in advertise to generate demand. First, we showed that average prices with mass advertising (nondiscrimination) are below those with targeted advertising. This is an interesting …nding as it challenges the usual …nding that price discrimination may reduce all segment prices. Second, we showed that price discrimination by means of targeted informative advertising do not necessarily lead to the classic prisoner dilemma result that arises in models with full informed consumers. In this way we showed that at least when v is high and advertising is not expensive each …rm’s pro…t with perfect targeted advertising and price discrimination is above its non-discrimination counterpart. Finally, another theme of the paper was to investigate the welfare e¤ects of targeted advertising with price discrimination in comparison to the mass advertising/non-discrimination case. We showed that at least when advertising costs are not too high in comparison to v; price discrimination by means of targeted advertising can boost industry pro…t at the expense of consumer surplus and welfare. Thus, the paper has highlighted the importance of taking into 28
account di¤erent forms of market competition when public policy tries to evaluate the pro…t and welfare e¤ects of price discrimination.
Appendix
Look …rst at case (i). Suppose (v; v) is an equilibrium in pure
Proof of Proposition 1. strategies. Then
1 = v i (1 j) + i j : 2 Any price greater than v is not part of an equilibrium strategy since such price is higher than consumers’reservation price for the most preferred good and therefore no consumer would be interested in buying the good and …rms would not make any pro…t. Any price lower than v but greater than v gives …rm i the same market share but reduces its pro…t and so it is dominated by v: If …rm i deviates and chooses price v it gets the remaining group of captive consumers and its pro…t from deviation is i
d i
= (v
The …rm has no incentive to deviate to v (v
")
i (1
i (1
")
j)
+
i j
as long as
j)
+
1 < v 2
i j
i (1
j)
+
i j
;
which requires: v
">
2
2 It is straightforward to see that the deviation is not pro…table if v < 2 : In contrast it is pro…table if v > 2 as such an " always exists. Therefore, when v < 2 ; (v; v) is a Nash equilibrium in pure strategies. (ii) Look next in the case where v > 2 and investigate in which conditions (v ;v ) is an equilibrium in pure strategies. In this case i
= (v
)
i (1
j)
+
1 2
i j
If …rm i deviates to a higher price it must be to price v: In this case, deviation pro…ts are equal to 1 1 d i (1 j) + i j = v i i = v 2 2 Firm i has an incentive to deviate i¤ 1 v 2
i
> (v
)
i (1
j)
which holds as long as: j
>1
v
29
:
+
1 2
i j
;
This means that for (v
;v
) to be a price equilibrium in pure strategies: 0
p
(
2+1) : 4
m
to be positive; the numerator of p ( 2+1) m must also be negative. This is always the case when > : In fact, the polyno4 p p p 2 1 ( ) ( 2+1) 1 2 mial 2 + 16 8 8 + 2 has three roots, 8 ; ; and : Furthermore: 4 4 p p ( 2+1) lim !+1 2 2 + 16 8 + 2 = 1: Accordingly, for > 8 ; both the numer4 m ator and the denominator of are negative and the ratio is positive. m For the condition < 1 to hold, it must be the case that: 2
For
>
p
(
2+1) 4
2
Then, for
p 8 + 16 8 2+8 16
+ 2
2
< 1:
the previous condition is equivalent to: 2
2
+ 16
which is always the case for p p 8 8 + 2 are 14 2 +1:
> 1
Proof of Proposition 5.
8 p
p 8
+
2
>
2
+8
16
2
;
2+1) ; given that the roots of the polynomial 2 +8 4 p and 14 2 + 1 , with lim !+1 2 + 8 + 16 2
(
+16 p 8 8
2
+
(Introduce proof)
Proof of Proposition 6. Next we prove that there is an equilibrium in mixed strategies in prices for an interior pure strategy equilibrium in advertising. Suppose that, in segment a; …rm A selects a price randomly from the cdf FAo (p) while …rm B selects a price randomly from the cdf FBr (p): We concentrate on symmetric MSNE in prices, in which FAo (p) = FBo (p) = F o (p) ; and FBr (p) = FAr (p) = F r (p) : Accordingly, for the sake of simplicity, we restrict our attention to …rms’decisions in segment A; obtaining FAo (p) = F o (p) and FBr (p) = F r (p) : Given …rm A’s pricing and advertising strategies to segment a, poA and oA ; resp., …rm A’s expected pro…t in segment A, denoted E oA is equal to E
o A
= poA
1 2
o A (1
+
1 2
+
1 2
r B)
o r A B
Pr(poA < prB + )
A(
o A)
A(
o A) :
or equivalently, E
A
= poA
1 2
o A (1
r B)
o r A B
34
[1
FBr (poA
)]
2
=
r ; B
Similarly …rm B’s expected pro…t in segment a, denoted E r B
E
1 = prB [ 2
r B (1
o A)
r o r B A Pr (pB
+
is
< poA )]
+
A(
r B)
or, 1 o r o = prB f rB (1 FAo (prB + )]g A ( rB ) : A ) + B A [1 2 Note that the minimum price …rm B is willing to charge even if it is assured of getting the entire segment of selective customers in market A should satisfy the following condition r B
E
1 r p [ 2 B min
r o B A
r B (1
+
o A )]
=
1 (v 2
r B (1
)
o A)
from which we obtain: prB min = (v
o A );
) (1
(32)
which corresponds to the expression of prB min pointed out in the Proposition. Given that …rm B would never want to price below prB min ; we observe that it is a dominated strategy for …rm A to price below prB min + : Thus, the support of equilibrium prices for …rm A is [prB min + ; v] while for …rm B is [prB min ; v ] As usual in a MSNE each …rm must be indi¤erent between charging any price in the support of equilibrium prices. For …rm B we must observe that for any prB min prB v : 1 r p f 2 B 1 (v 2
=
r B (1
)
o A)
r o B A [1
+
r B (1
o A)
A(
FAo (prB + )]g
1
(v
1
o A
1 o A
(v
1
o A)
) (1 p
or, equivalently to FAo (p) =
r B)
r B)
which simpli…es to FAo (p + ) =
A(
) (1 p
o A)
where FAo (v) = 1: Note also that FAo (pB min + ) = 0. In this way 8 > 0 p prB min + > < h i if o (v )(1 A ) 1 FAo (p) = 1 if prB min + p o p A > > : 1 if p v
v
9 > > = > > ;
;
which corresponds to the specifcation of Fio (p) presented in the Proposition. Analogously, for …rm A we must observe that for any prB min + poA v : E
o A
= poA
= (prB min + )
1 2
o A (1
1 2
o A (1
r B)
+
r B)
1 2
+
o r A B
1 2
35
[1
o r A B
FBr (poA A(
o A)
)]
A(
o A)
or poA =
1 2
1 2
o A (1
o r A (pB min
r B)
1 2
+
+ )
o r A B
A(
1
)=
r B
1 r B
1
FBr (p) =
r B
1
A(
o A)
prB min + p
1
or, FBr (p) =
)]
o A)
This simpli…es to FBr (p
FBr (poA
[1
prB min + p+
1
o A)
v (1
+
o A
p+
As expected note that FBr (pB min ) = 0: Thus, the corresponding distribution is 8 9 r > > 0 if p p > > B min > > < = o o v (1 A )+ A r 1 r 1 if p p v FB (p) = ; r B min p+ B > > > > > > : ; 1 if p v
which corresponds to the expression of Fir (p) pointed out in the Proposition. Firm A0 s expected pro…t when charging any price in the support of equilibrium prices is equal to: 1 o (v (v ) oA ) A ( oA ) : E A= 2 A From the previous expression it follows that E A depends on oA . The pro…t-maximizing ad@2E A A vertising intensity is obtained from the condition @E < 0: Accordingly, the @ oA = 0; since @ o2 A optimal advertising intensity is implicitly given by the condition: 1 v |2
which can also be written as:
A (v
)=A }
{z
M RAo
o A
o A) ;
(
1 = A oA ( oA ) 2v Given …rm B’s expected pro…t in the MSNE given by poA min
E
B
=
1 (v 2
)
r B (1
o A)
A(
r B) ;
the following …rst order condition de…nes …rm B 0 s optimal advertising level in segment a @E B 1 = 0 ) (v r @ B 2 since the second order condition written as
@2E A @ o2 A
o A)
) (1
=A
r B
(
r B) ;
< 0 is always met. This condition may be alternatively
1 r p =A 2 j min 36
r i
r i
:
(33)
Firm i0 s pro…t conditional on ads targeted to its own market and to the rival’s market is: E
i
o
=
i
E
o
A
i
r
1 ( o )2 (v 2 A = i rA i r ( i r) A ( i
o
(
i
o
)+
) i
r
A(
o A)
(34)
):
(35)
Proof of Proposition 7. The …rst part of proposition 7 follows directly from the equilibrium condition with respect to oi : When advertising is costless, this condition writes as:
o A
1 v 2 |
v 2(v
A (v {z
) = 0; }
M RAo
yielding = ) ; which is always smaller than 1 for v > 2 : The second part of the propostion follows directly from plugging the equilibrium value of prmin (computed in the Proof of Proposition 6) into the conditions prmin S v 2 :
Proof of Corollary 1. From Proposition 2, it follows that Fir (v is always smaller than 1 when
o i
0 and that oi < 1 as long as v > 2 : )(v+4 2 ) From rj = (v 8 (v+2 it follows that rj > 0 i¤ v > 2 : Look next in which circum) stances we obtain rj < 1: From (v we obtain
v2 p
4v
(5v 9 )(v
) (v + 4 8 (v + 2 3v 16 8 (v + 2 ) (v
2 ) 5 ; which is true under the assumption that v > 2 :
2(v
Proof of Proposition 9. )(v+4 r v = (v 8 (v+2 )+4 and o
r
=
9 > 0 or when
From Proposition 8 we obtain the optimal values of 2 ) ) : The …rm advertises more in its own market if: v 2 (v
(v )+4
) (v + 4 8 (v + 2
This is equivalent to: 1 3v + 2 2 4 + v 2 8 (v + 2 )
37
0
2 ) )
0;
o
=
or
3v + 2
2
o
+ v 2 < 0:Solving for v; we obtain that
4
1p 2
3 2
v2
2
+ 16
;
3 1p + 2 2
2
r
0 if
+ 16
p 1 2 + 16 < 2 : Since we have imposed v > 2 However, it can be easily seen that 32 2 in order to concentrate on interior solutions in the advertising market, under v > 2 ; we have r that o > 0 if p 1 2 + 16 2 2 :
Each …rm serves its group of selective customers at po with
Proof of Proposition 10. probability given by 2 [0; 1]: =
Z
Z
v
pR min
pB +
pomin
f (pA ) dpA
!
f (pB ) dpB ;
or equivalently: =
Z
v
pR min
Z
pB +
(v
) (x 2
x (p
pomin
1) )
!
dp
x
v (x 1) y (p + )2
dpB ;
which is equivalent to: =
v r
v
1
1 o
o
(v
)
2 pr min
v
(v
pomin ) + v (
pomin ) ln
pomin v prmin v
;
since pomin = prmin + :
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